[Tomnavigator]

I know this is late to help you now. Regular a/c compressor failures are not caused by the high heat in arizona. If this were true, then all cars would be having a/c compressor failures not just your BMW. The primary cause of multiple a/c compressor failures are one or more of the following.

But, regular failure of an a/c compressor is caused by one or both of two things.
1) When an a/c compressor fails, debris is deposited in the lines. If this debris is not flushed out of the system, any new compressor will fail. To check to see if this is an issue, the next time the compressor fails have the shop show you the capillary tube. The capillary tube has a filter in front of it. Look and see if the filter is clean or contaminated. If contaminated, the system is not clean. Thus causing compressor failure.
2) The second cause of compressor failures is improper oil or lack of oil in the system. This is unlikely since the compressor has been replaced multiple times. There may be too much oil in the system if oil has been added every time the compressor has been replaced. Next time the compressor is replaced make sure the system is flushed and the correct amount of oil is added when the compressor is replaced.
3) Excessive liquid in the system reaching the compressor causes compressor failure. Liquid is not compressible and will destroy an a/c compressor quickly. Water or oil typically. In arizona I doubt it is water.